Average Error: 0.2 → 0.1
Time: 11.2s
Precision: 64
\[\left(x \cdot x\right) \cdot \left(3 - x \cdot 2\right)\]
↓
\[x \cdot \left(3 \cdot x\right) + \left(-2 \cdot {x}^{3}\right)\]
\left(x \cdot x\right) \cdot \left(3 - x \cdot 2\right)
↓
x \cdot \left(3 \cdot x\right) + \left(-2 \cdot {x}^{3}\right)
double f(double x) {
        double r797888 = x;
        double r797889 = r797888 * r797888;
        double r797890 = 3.0;
        double r797891 = 2.0;
        double r797892 = r797888 * r797891;
        double r797893 = r797890 - r797892;
        double r797894 = r797889 * r797893;
        return r797894;
}
↓
double f(double x) {
        double r797895 = x;
        double r797896 = 3.0;
        double r797897 = r797896 * r797895;
        double r797898 = r797895 * r797897;
        double r797899 = 2.0;
        double r797900 = 3.0;
        double r797901 = pow(r797895, r797900);
        double r797902 = r797899 * r797901;
        double r797903 = -r797902;
        double r797904 = r797898 + r797903;
        return r797904;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.2
Target0.2
Herbie0.1
\[x \cdot \left(x \cdot \left(3 - x \cdot 2\right)\right)\]

Derivation

  1. Initial program 0.2

    \[\left(x \cdot x\right) \cdot \left(3 - x \cdot 2\right)\]
  2. Using strategy rm

  3. Applied associate-*l*0.2

    \[\leadsto \color{blue}{x \cdot \left(x \cdot \left(3 - x \cdot 2\right)\right)}\]
  4. Using strategy rm

  5. Applied sub-neg0.2

    \[\leadsto x \cdot \left(x \cdot \color{blue}{\left(3 + \left(-x \cdot 2\right)\right)}\right)\]

  6. Applied distribute-lft-in0.2

    \[\leadsto x \cdot \color{blue}{\left(x \cdot 3 + x \cdot \left(-x \cdot 2\right)\right)}\]

  7. Applied distribute-lft-in0.2

    \[\leadsto \color{blue}{x \cdot \left(x \cdot 3\right) + x \cdot \left(x \cdot \left(-x \cdot 2\right)\right)}\]

  8. Simplified0.2

    \[\leadsto \color{blue}{x \cdot \left(3 \cdot x\right)} + x \cdot \left(x \cdot \left(-x \cdot 2\right)\right)\]

  9. Simplified0.1

    \[\leadsto x \cdot \left(3 \cdot x\right) + \color{blue}{\left(-2 \cdot {x}^{3}\right)}\]

  10. Final simplification0.1

    \[\leadsto x \cdot \left(3 \cdot x\right) + \left(-2 \cdot {x}^{3}\right)\]

Reproduce

herbie shell --seed 2020045 
(FPCore (x)
  :name "Data.Spline.Key:interpolateKeys from smoothie-0.4.0.2"
  :precision binary64

  :herbie-target
  (* x (* x (- 3 (* x 2))))

  (* (* x x) (- 3 (* x 2))))